How much is your Strangle worth? On the relative value of the $δ-$Symmetric Strangle under the Black-Scholes model

Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. In this paper we propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes option pricing model. This new measure accounts for the price of the strangle, relative to the Present Value of the spread between the two strikes, all expressed, after a natural re-parameterization, in terms of delta and a volatility parameter. We show that under the standard BS option pricing model, this measure of relative value is bounded by a simple function of delta only and is independent of the time to expiry, the price of the underlying security or the prevailing volatility used in the pricing model. We demonstrate how this bound can be used as a quick {\it benchmark} to assess, regardless the market volatility, the duration of the contract or the price of the underlying security, the market (relative) value of the $\delta-$strangle in comparison to its BS (relative) price. In fact, the explicit and simple expression for this measure and bound allows us to also study in detail the strangle's exit strategy and the corresponding {\it optimal} choice for a value of delta.